Gritsenko Oleg, Baerends Evert Jan
Theoretische Chemie, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands.
J Chem Phys. 2004 Jul 8;121(2):655-60. doi: 10.1063/1.1759320.
Time-dependent density functional theory (TDDFT) calculations of charge-transfer excitation energies omegaCT are significantly in error when the adiabatic local density approximation (ALDA) is employed for the exchange-correlation kernel fxc. We relate the error to the physical meaning of the orbital energy of the Kohn-Sham lowest unoccupied molecular orbital (LUMO). The LUMO orbital energy in Kohn-Sham DFT--in contrast to the Hartree-Fock model--approximates an excited electron, which is correct for excitations in compact molecules. In CT transitions the energy of the LUMO of the acceptor molecule should instead describe an added electron, i.e., approximate the electron affinity. To obtain a contribution that compensates for the difference, a specific divergence of fxc is required in rigorous TDDFT, and a suitable asymptotically correct form of the kernel fxc(asymp) is proposed. The importance of the asymptotic correction of fxc is demonstrated with the calculation of omegaCT(R) for the prototype diatomic system HeBe at various separations R(He-Be). The TDDFT-ALDA curve omegaCT(R) roughly resembles the benchmark ab initio curve omegaCT CISD(R) of a configuration interaction calculation with single and double excitations in the region R=1-1.5 A, where a sizable He-Be interaction exists, but exhibits the wrong behavior omegaCT(R)<<omegaCT CISD(R) at large R. The TDDFT curve obtained with fxc (asymp) however approaches omegaCT CISD(R) closely in the region R=3-10 A. Then, the adequate rigorous TDDFT approach should interpolate between the LDA/GGA ALDA xc kernel for excitations in compact systems and fxc(asymp) for weakly interacting fragments and suitable interpolation expressions are considered.
当采用绝热局域密度近似（ALDA）处理交换关联核fxc时，基于含时密度泛函理论（TDDFT）对电荷转移激发能ωCT的计算存在显著误差。我们将该误差与Kohn-Sham最低未占据分子轨道（LUMO）的轨道能量的物理意义联系起来。与Hartree-Fock模型不同，Kohn-Sham密度泛函理论中的LUMO轨道能量近似一个激发电子，这对于紧密分子中的激发是正确的。在电荷转移跃迁中，受体分子LUMO的能量反而应描述一个添加电子，即近似电子亲和能。为了获得补偿这种差异的贡献，严格的TDDFT需要fxc的特定发散形式，并提出了一种合适的渐近正确的核fxc(asymp)形式。通过计算原型双原子体系HeBe在不同间距R(He-Be)下的ωCT(R)，证明了fxc渐近修正的重要性。TDDFT-ALDA曲线ωCT(R)在R = 1 - 1.5 Å区域大致类似于单双激发组态相互作用计算的基准从头算曲线ωCT CISD(R)，该区域存在可观的He-Be相互作用，但在大R时表现出错误的行为ωCT(R) << ωCT CISD(R)。然而，用fxc(asymp)得到的TDDFT曲线在R = 3 - 10 Å区域与ωCT CISD(R)非常接近。然后，适当的严格TDDFT方法应在紧密体系激发的LDA/GGA ALDA xc核与弱相互作用片段的fxc(asymp)之间进行插值，并考虑合适的插值表达式。
